Zimbra server process is running as uid=500 euid=500 gid=500 egid=500
Total time for which application threads were stopped: 0.0001690 seconds
Total time for which application threads were stopped: 0.0002750 seconds
Total time for which application threads were stopped: 0.0020620 seconds
Fatal error: terminating: cannot initialize RightManager
com.zimbra.common.service.ServiceException: parse error: root tag is not rights

Are you running as the Zimbra user?

Also,

It would help if you gave what distro you're using and what version of Zimbra